# clifford.BasisVectorIds¶

Stores ids for the ordered set of basis vectors, typically integers.

Provides helpers to convert between bitmaps indicating which vectors are present in a blade, and tuples of the original ids.

For example:

```>>> ids = BasisVectorIds([11, 22, 33])
>>> ids.bitmap_as_tuple(0b110)
(22, 33)
>>> sign, bitmap = ids.tuple_as_sign_and_bitmap((33, 22))
>>> assert sign, bitmap == (-1, 0b110)
```
bitmap_as_tuple(bitmap: int)Tuple[clifford._layout_helpers.IdT][source]

Convert a bitmap representation into a tuple of ids.

id_as_bitmap(id: clifford._layout_helpers.IdT)int[source]

Convert the id of a single vector into a bitmap representation.

Convert a blade from a tuple of ids into a bitmap representation.

Produce an ordering from a set of tuples.

This is the inverse of `order_as_tuples()`.

```>>> ids = BasisVectorIds(['x', 'y'])
>>> ids.order_from_tuples([(), ('y',), ('x', 'y'), ('x',)])
BasisBladeOrder([0b00, 0b10, 0b11, 0b01])
```

Represent an ordering with these ids.

This is the inverse of `order_from_tuples()`.

```>>> ids = BasisVectorIds(['x', 'y'])
>>> ids.order_as_tuples(BasisBladeOrder([0b00, 0b10, 0b11, 0b01]))
[(), ('y',), ('x', 'y'), ('x',)]
```
classmethod ordered_integers(n: int, *, first_index: int = 1)clifford._layout_helpers.BasisVectorIds[int][source]

Create a set of n sequential integers as ids, starting from first_index.

augmented_with(n: int)clifford._layout_helpers.BasisVectorIds[source]

Return a new copy with n new ids at the end.